No, not in their present forms.
The problem is that convex loss functions cannot be made to be robust to contamination by outliers (this is a well known fact since the 70's but keeps being rediscovered periodically, see for instance this paper for one recent such re-discovery):
Now, in the case of regression trees, the fact that CART uses marginals (or alternatively univariate projections) can be used:
one can think of a version of CART where the s.d. criterion is replaced by a more
robust counterpart (MAD or better yet, Qn estimator).
I recently came across an older paper implementing the approach suggested above (using robust M estimator of scale instead of the MAD). This will impart robustness to "y" outliers to CART/RF's (but not to outliers located on the design space, which will affect the estimates of the model's hyper-parameters) See:
Galimberti, G., Pillati, M., & Soffritti, G. (2007). Robust regression trees based on M-estimators.
Statistica, LXVII, 173–190.